Упр.870 ГДЗ Алимов 10-11 класс (Алгебра)

2) cosx-lnx;
3) sinx- корень 3 степени x;
4) 6×4-9ex;
5) 5/x + 4e4;
6) 1/3×3 + 1lnx/2.

1. $$f(x)=e^x-\sin x$$

   $$f'(x)=(e^x)’-(\sin x)’=e^x-\cos x$$

2. $$f(x)=\cos x-\ln x$$

   $$f'(x)=(\cos x)’-(\ln x)’=-\sin x-\frac{1}{x}$$

3. $$f(x)=\sin x-\sqrt[3]{x}$$

   $$f'(x)=(\sin x)’-(x^{1/3})’=\cos x-\frac{1}{3}x^{-2/3}=\cos x-\frac{1}{3\sqrt[3]{x^2}}$$

4. $$f(x)=6x^4-9e^x$$

   $$f'(x)=(6x^4)’- (9e^x)’=24x^3-9e^x$$

5. $$f(x)=\frac{5}{x}+4e^x$$

   $$f'(x)=5\left(\frac{1}{x}\right)’+4(e^x)’=-\frac{5}{x^2}+4e^x$$

6. $$f(x)=\frac{1}{3x^3}+\frac{1}{2}\ln x$$

   $$f'(x)=\frac{1}{3}(x^{-3})’+\frac{1}{2}(\ln x)’=\frac{1}{3}\cdot(-3)x^{-4}+\frac{1}{2}\cdot\frac{1}{x}=-\frac{1}{x^4}+\frac{1}{2x}$$

Ответ

1. $$e^x-\cos x$$
2. $$-\sin x-\frac{1}{x}$$
3. $$\cos x-\frac{1}{3\sqrt[3]{x^2}}$$
4. $$24x^3-9e^x$$
5. $$-\frac{5}{x^2}+4e^x$$
6. $$-\frac{1}{x^4}+\frac{1}{2x}$$